In geometry, an icosahedron is a polyhedron that is comprised of twenty faces. In a “regular” icosahedron each of the twenty faces forms an equilateral triangle. The regular icosahedron is one of the five Platonic solids, which have long since been recognized and appreciated by mathematicians for their aesthetic beauty and symmetry. The other four Platonic solids are a regular tetrahedron (pyramid with all faces being equilateral triangles), a regular hexahedron (cube), a regular octahedron (eight-sided figure with all faces being equilateral triangles), and a regular dodecahedron (twelve-sided figure with pentagonal faces).
A “truncated” icosahedron can be constructed from an icosahedron cutting off the 12 vertices of the icosahedron such that each edge is cut off at both ends. This creates 12 new pentagon faces and leaves the original 20 triangle faces as regular hexagons. Thus, the truncated icosahedron has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges.